Question 7
1a. (CZS 3) The positive integers $x_1,\ldots,x_n$, $n\ge3$, satisfy $x_1\lt x_2\lt \cdots\lt x_n\lt 2x_1$. Set $P=x_1x_2\cdots x_n$. Prove that if $p$ is a prime number, $k$ a positive integer, and $P$ is divisible by $p^k$, then $\frac P{p^k}\ge n!$.